Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $6^{4}\cdot24^{2}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24D4 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&27\\36&77\end{bmatrix}$, $\begin{bmatrix}49&25\\88&71\end{bmatrix}$, $\begin{bmatrix}107&93\\108&41\end{bmatrix}$, $\begin{bmatrix}111&50\\4&63\end{bmatrix}$, $\begin{bmatrix}115&48\\28&83\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.4.fa.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.72.2-24.j.1.13 | $24$ | $2$ | $2$ | $2$ | $0$ |
| 120.72.2-24.j.1.6 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.48.0-120.ba.1.1 | $120$ | $3$ | $3$ | $0$ | $?$ |
| 120.72.2-120.cx.1.7 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.cx.1.26 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.dh.1.7 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.dh.1.42 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.288.7-120.bnn.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bnp.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bnw.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bnz.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bok.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bon.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.boz.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bpe.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bpp.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bpu.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bqg.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bqj.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bqr.1.5 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bqt.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bqz.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.brb.1.1 | $120$ | $2$ | $2$ | $7$ |